a(n) = n*binomial(2n, n) - 4^n.

Terms

a(0) =-1a(1) =-2a(2) =-4a(3) =-4a(4) =24a(5) =236a(6) =1448a(7) =7640a(8) =37424a(9) =175436a(10) =798984a(11) =3565448a(12) =15672656a(13) =68098936a(14) =293196944a(15) =1253020976a(16) =5322318944a(17) =22491436556a(18) =94632958664a(19) =396682105256